For many materials, including practically every man-made synthetic material, the mechanical behavior during processing as well as end product conditions is an important parameter that must be tightly specified and controlled. During the initial phases in the development of a new polymer or process, an understanding of the relationship between chemical structure and the physical properties of the process is of vital concern. Later on, in the process and quality control stages, factors such as mechanical strength, dimensional and thermal stability, and impact resistance are of utmost importance.
Virtually all synthetic materials in existence are viscoelastic, i.e., their behavior under mechanical stress lies somewhere between that of a purely viscous liquid and that of a perfectly elastic spring. Few materials behave like a perfect spring or a pure liquid. Rather, the mechanical behavior of these materials is generally time and/or temperature dependent and has led to such tests as creep, stress relaxation, tear, impact resistance, etc. One of the more important properties of materials sought is the materials' behavior under dynamic conditions. To explore this, a material's response to a cyclical stress as a function of temperature, time or frequency is determined. If a sample of a viscoelastic solid, for example, is deformed and then released, a portion of the stored deformation energy will be returned at a rate which is a fundamental property of the material. That is, the sample goes into damped oscillation. A portion of the deformation energy is dissipated in other forms. The greater the dissipation, the faster the oscillation dies away. If the dissipated energy is restored, the sample will vibrate at its natural (resonant) frequency. The resonant frequency is related to the modulus (stiffness) of the sample. Energy dissipation relates to such properties as impact resistance, brittleness, noise abatement, etc.
Because of their viscoelastic nature, the stress and strain in viscoelastic materials are not in phase, and, in fact, exhibit hysteresis. If a plot is made of this relationship, the area enclosed by the plot corresponds to the energy dissipated during each cycle of deformation of the material. In order to accurately describe this phenomenon, a complex modulus E=E'+jE" is often used to characterize the material where E is Young's modulus, E' is the real part and E" is the imaginary part. The real part E' of the modulus corresponds to the amount of energy that is stored in the strain and can be related to the spring constant, the complex part E" corresponds to the energy dissipation or loss and can be related to the damping coefficient used in second order differential equations to define vibrating systems.
Many mechanical analyzers have been developed for testing and ascertaining such properties as the loss modulus and elastic modulus of materials and the variations of these properties as a function of both time and temperature. Among these systems are those described for example in U.S. Pat. Nos. 3,501,952 issued Mar. 24, 1970 to Gergens et al.; 3,508,437 issued Apr. 27, 1970 to Van Beek; 3,751,977 issued Aug. 14, 1973 to Schilling; 4,034,602 issued July 12, 1977 to Woo et al. and 4,049,997 issued Sept. 20, 1977 to McGhee. All of these systems place the sample under test into vibration or oscillation utilizing mechanical systems. These mechanical systems vibrate at a resonant frequency determined primarily by the sample. A drive transducer is used to maintain the system in oscillation, a displacement transducer is used to sense the displacement of the mechanical system, and a drive amplifier is used to energize the drive transducer sufficiently to maintain the system oscillating at resonance at a constant amplitude.
While many of these systems attempt to measure the elastic modulus (E'), the loss modulus (E") is typically measured only on a relative basis by sensing the power input to the system that is required to maintain a constant oscillation amplitude. Unfortunately this does not provide a calibrated result in commonly accepted units. Other methods of determining the loss modulus are by obtaining the logarithmic decrement by free decay of the system. Unfortunately, this requires substantial additional instrumentation. Another method of determining loss modulus is to use the second order relationship that exists between oscillation frequency and amplitude. This approach, while satisfactory, does not always provide the results of the quality that might be desired.
Accordingly it is an object of this invention to overcome many of the disadvantages of the prior art methods for obtaining the loss modulus of materials.
Another object of this invention is to provide an improved method of obtaining the loss modulus of materials.
A further object of this invention is to provide an improved apparatus for ascertaining the loss modulus of materials.